That is because Sachin led with an example (realized so early in the history of T20) that T20 is a game for youngsters! So he stayed away from that format (International T20) right from the beginning. Result: young team played ruthless cricket and won the world cup! But after the advent of IPL, senior cricketers (including Tendulkar) got to play in IPL T20. Instead of sticking to IPL (a neat pension job giving everything like fame/brand retention, money, rest, entertainment/recreation after retirement, etc), these seniors (e.g., Karthik) made way back to LOI World Cups through backdoors somehow!
Especially T20 is such a format that every year almost half of the team should change with younger players (you will see the glimpse of that when you observe teams from SENA every year) But you are seeing Karthiks being part of it for like 15 years! Ideally even Rohit, Rahul, Shami, Bhuvaneshwar, Ashwin, etc, should not be playing T20s... (Even Kohli & Bumrah can concentrate more on Tests & ODIs. Other hunger youngsters can easily handle T20 games!)
Every year young guns like Suryakumar, Arshdeep should keep coming and should keep getting discovered! A young team led by H.Pandya would have fared much better (like his team did in last IPL though his team too had seniors, but they were present in other teams also so it evened out! But their approach & composition were much better than other teams!) The average age of players in a T20 team should be well within 25-30 years! Even ODIs need to follow this suit slightly (but players like Kohli, Rohit, Rahul, etc, can get into that format. But Karthiks no way in anything!) Tests is where seniors (like Anderson, Root, etc) belong! But in India strangely our "Test Team" (with Pant) looks lot younger than LOI teams! (Last success in Australia was best example of this)
There are other reasons also for this. Last game against South Africa we lost the match because of another factor (fielding). Rohit, Rahul & Kohli were not up to the intensity of the game (spilled chances). T20 is a game where things happen so quickly & magic should be created suddenly and the players should be on their toes, eager & hunger for any opportunity! They should search for creating chances every time! If pitch is difficult to bat, they should run hard and keep scoring...
And don't blame IPL blindly for everything. IPL is there for some purpose which needs to be utilized properly! Every year we see lots of promising players but none of them feature more in international cricket. The stupid rotation policy is not helping either. (e.g., Dhawan making comebacks!) Unless we understand how we should be framing a T20 team, nothing will change!